What is meant by "the number of examples is reduced", and why is this the case?
I think what he means is that, while distribution $P(y  \mid x,s)$ has three variables, $P(y  \mid x)$ has two variables. The number of parameters required to describe a distribution (or samples to approximate it) grows exponentially with the number of variables (for more info see for instance Ian goodfellow, .. deep learning&quot;).